{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2023 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# assignment_groups_mip"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/linear_solver/assignment_groups_mip.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/ortools/linear_solver/samples/assignment_groups_mip.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "Solve assignment problem for given group of workers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ortools.linear_solver import pywraplp\n",
    "\n",
    "\n",
    "def main():\n",
    "    # Data\n",
    "    costs = [\n",
    "        [90, 76, 75, 70, 50, 74],\n",
    "        [35, 85, 55, 65, 48, 101],\n",
    "        [125, 95, 90, 105, 59, 120],\n",
    "        [45, 110, 95, 115, 104, 83],\n",
    "        [60, 105, 80, 75, 59, 62],\n",
    "        [45, 65, 110, 95, 47, 31],\n",
    "        [38, 51, 107, 41, 69, 99],\n",
    "        [47, 85, 57, 71, 92, 77],\n",
    "        [39, 63, 97, 49, 118, 56],\n",
    "        [47, 101, 71, 60, 88, 109],\n",
    "        [17, 39, 103, 64, 61, 92],\n",
    "        [101, 45, 83, 59, 92, 27],\n",
    "    ]\n",
    "    num_workers = len(costs)\n",
    "    num_tasks = len(costs[0])\n",
    "\n",
    "    # Allowed groups of workers:\n",
    "    group1 = [  # Subgroups of workers 0 - 3\n",
    "        [2, 3],\n",
    "        [1, 3],\n",
    "        [1, 2],\n",
    "        [0, 1],\n",
    "        [0, 2],\n",
    "    ]\n",
    "\n",
    "    group2 = [  # Subgroups of workers 4 - 7\n",
    "        [6, 7],\n",
    "        [5, 7],\n",
    "        [5, 6],\n",
    "        [4, 5],\n",
    "        [4, 7],\n",
    "    ]\n",
    "\n",
    "    group3 = [  # Subgroups of workers 8 - 11\n",
    "        [10, 11],\n",
    "        [9, 11],\n",
    "        [9, 10],\n",
    "        [8, 10],\n",
    "        [8, 11],\n",
    "    ]\n",
    "\n",
    "    # Solver.\n",
    "    # Create the mip solver with the SCIP backend.\n",
    "    solver = pywraplp.Solver.CreateSolver(\"SCIP\")\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    # Variables\n",
    "    # x[worker, task] is an array of 0-1 variables, which will be 1\n",
    "    # if the worker is assigned to the task.\n",
    "    x = {}\n",
    "    for worker in range(num_workers):\n",
    "        for task in range(num_tasks):\n",
    "            x[worker, task] = solver.BoolVar(f\"x[{worker},{task}]\")\n",
    "\n",
    "    # Constraints\n",
    "    # The total size of the tasks each worker takes on is at most total_size_max.\n",
    "    for worker in range(num_workers):\n",
    "        solver.Add(solver.Sum([x[worker, task] for task in range(num_tasks)]) <= 1)\n",
    "\n",
    "    # Each task is assigned to exactly one worker.\n",
    "    for task in range(num_tasks):\n",
    "        solver.Add(solver.Sum([x[worker, task] for worker in range(num_workers)]) == 1)\n",
    "\n",
    "    # Create variables for each worker, indicating whether they work on some task.\n",
    "    work = {}\n",
    "    for worker in range(num_workers):\n",
    "        work[worker] = solver.BoolVar(f\"work[{worker}]\")\n",
    "\n",
    "    for worker in range(num_workers):\n",
    "        solver.Add(\n",
    "            work[worker] == solver.Sum([x[worker, task] for task in range(num_tasks)])\n",
    "        )\n",
    "\n",
    "    # Group1\n",
    "    constraint_g1 = solver.Constraint(1, 1)\n",
    "    for i in range(len(group1)):\n",
    "        # a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]\n",
    "        # p is True if a AND b, False otherwise\n",
    "        constraint = solver.Constraint(0, 1)\n",
    "        constraint.SetCoefficient(work[group1[i][0]], 1)\n",
    "        constraint.SetCoefficient(work[group1[i][1]], 1)\n",
    "        p = solver.BoolVar(f\"g1_p{i}\")\n",
    "        constraint.SetCoefficient(p, -2)\n",
    "\n",
    "        constraint_g1.SetCoefficient(p, 1)\n",
    "\n",
    "    # Group2\n",
    "    constraint_g2 = solver.Constraint(1, 1)\n",
    "    for i in range(len(group2)):\n",
    "        # a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]\n",
    "        # p is True if a AND b, False otherwise\n",
    "        constraint = solver.Constraint(0, 1)\n",
    "        constraint.SetCoefficient(work[group2[i][0]], 1)\n",
    "        constraint.SetCoefficient(work[group2[i][1]], 1)\n",
    "        p = solver.BoolVar(f\"g2_p{i}\")\n",
    "        constraint.SetCoefficient(p, -2)\n",
    "\n",
    "        constraint_g2.SetCoefficient(p, 1)\n",
    "\n",
    "    # Group3\n",
    "    constraint_g3 = solver.Constraint(1, 1)\n",
    "    for i in range(len(group3)):\n",
    "        # a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]\n",
    "        # p is True if a AND b, False otherwise\n",
    "        constraint = solver.Constraint(0, 1)\n",
    "        constraint.SetCoefficient(work[group3[i][0]], 1)\n",
    "        constraint.SetCoefficient(work[group3[i][1]], 1)\n",
    "        p = solver.BoolVar(f\"g3_p{i}\")\n",
    "        constraint.SetCoefficient(p, -2)\n",
    "\n",
    "        constraint_g3.SetCoefficient(p, 1)\n",
    "\n",
    "    # Objective\n",
    "    objective_terms = []\n",
    "    for worker in range(num_workers):\n",
    "        for task in range(num_tasks):\n",
    "            objective_terms.append(costs[worker][task] * x[worker, task])\n",
    "    solver.Minimize(solver.Sum(objective_terms))\n",
    "\n",
    "    # Solve\n",
    "    print(f\"Solving with {solver.SolverVersion()}\")\n",
    "    status = solver.Solve()\n",
    "\n",
    "    # Print solution.\n",
    "    if status == pywraplp.Solver.OPTIMAL or status == pywraplp.Solver.FEASIBLE:\n",
    "        print(f\"Total cost = {solver.Objective().Value()}\\n\")\n",
    "        for worker in range(num_workers):\n",
    "            for task in range(num_tasks):\n",
    "                if x[worker, task].solution_value() > 0.5:\n",
    "                    print(\n",
    "                        f\"Worker {worker} assigned to task {task}.\"\n",
    "                        + f\" Cost: {costs[worker][task]}\"\n",
    "                    )\n",
    "    else:\n",
    "        print(\"No solution found.\")\n",
    "\n",
    "\n",
    "main()\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 5
}
